Quality of White Wines by Alan Gou
Preliminary Exploration
Before I begin plotting the data, I want to first figure out a couple of things about the variables. First, how many of each quality are there?
summary(wf)## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. : 3.800 Min. :0.0800 Min. :0.0000 Min. : 0.600
## 1st Qu.: 6.300 1st Qu.:0.2100 1st Qu.:0.2700 1st Qu.: 1.700
## Median : 6.800 Median :0.2600 Median :0.3200 Median : 5.200
## Mean : 6.855 Mean :0.2782 Mean :0.3342 Mean : 6.391
## 3rd Qu.: 7.300 3rd Qu.:0.3200 3rd Qu.:0.3900 3rd Qu.: 9.900
## Max. :14.200 Max. :1.1000 Max. :1.6600 Max. :65.800
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. :0.00900 Min. : 2.00 Min. : 9.0
## 1st Qu.:0.03600 1st Qu.: 23.00 1st Qu.:108.0
## Median :0.04300 Median : 34.00 Median :134.0
## Mean :0.04577 Mean : 35.31 Mean :138.4
## 3rd Qu.:0.05000 3rd Qu.: 46.00 3rd Qu.:167.0
## Max. :0.34600 Max. :289.00 Max. :440.0
## density pH sulphates alcohol
## Min. :0.9871 Min. :2.720 Min. :0.2200 Min. : 8.00
## 1st Qu.:0.9917 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.50
## Median :0.9937 Median :3.180 Median :0.4700 Median :10.40
## Mean :0.9940 Mean :3.188 Mean :0.4898 Mean :10.51
## 3rd Qu.:0.9961 3rd Qu.:3.280 3rd Qu.:0.5500 3rd Qu.:11.40
## Max. :1.0390 Max. :3.820 Max. :1.0800 Max. :14.20
## quality
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.878
## 3rd Qu.:6.000
## Max. :9.000table(wf$quality)##
## 3 4 5 6 7 8 9
## 20 163 1457 2198 880 175 5Dataset Information
There are 4898 observations of 12 variables. Each observation (or row) is 11 variables descirbing various chemical/physical aspects of a wine plus the median of the ratings given by judges of that wine, 0 being the lowest rating and 10 being the highest.
Goal of analyzing this dataset
Quality is the feature of interest - the goal of this analysis is to explore what other features of the data explain the quality the wines.
Some preliminary expectations
From what I have read in the readme for the dataset, I am expecting levels of sulfur dioxide to play a part in determining quality - it seems like there ought to be a balance of sulfur dioxide. Too much will cause a bad, sulfurous odor, while too little may make the wine not fresh. Beyond that, my non-existent knowledge of wine would have me expect that sugar levels, alcohol content, and salt content would all have some sort of effect on quality, though in what way I really have no idea at this point. I also expect acidity to be a factor in determining quality
Creating new ‘quality_level’ bucket
As you can see, there are no wines with ratings of 0, 1, 2, or 10. There are only 5 wines with ratings of 9 and 20 with ratings of 3. This seems like a good indication that I can group some of these variables together into buckets: “high”, “medium-high”, “medium”, “medium-low”, and “low”. I’ll do this by adding a new variable: quality_level. This will let me use geom_freqpoly and facet_wrap more effectively, since I won’t have one category with only 5 observations in it and another category with over 2000. Low is 3 and 4, medium low is 5, medium is 6, medium-high is 7, and high is 8 and 9.
This distribution is somewhat normal, though there are several hundred more medium-low wines than medium-high wines. Still, I think this will serve as a suitable replacement for quality in terms of plotting.
Exploration of distributions as related to quality
Here, I want to first plot the distributions of the data as they relate to quality to see if there is any variable that has visibly different distributions depending on the quality of the wine. If none are found, then I’ll have to drill down deeper to see which combinations of factors affect quality.
pH
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.720 3.090 3.180 3.188 3.280 3.820
##
## Pearson's product-moment correlation
##
## data: wf$pH and wf$quality
## t = 6.9917, df = 4896, p-value = 3.081e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.07162022 0.12707983
## sample estimates:
## cor
## 0.09942725pH is very normally distributed, with no outliers. This makes sense - a wine would have to be orders of magnitude more basic or more acidic to be an outlier in pH, which would probably mean it probably not be suitable for consumption. The mean pH is around 3.2, and most wines don’t vary too much from this.
I expected distinctive distribtuions of overall pH levels based on quality of wine, and the boxplot confirms my expectations. There seems to be a general rise in pH as quality increases, with the mean for low quality wines being below 3.2 and the mean for high quality wines being above 3.2. This means that more acidic wines tend to be rated lower. Whether this occurs as a side effect of the wine making process for making higher quality wines or because more basic wines just taste better is something that would require investigation into the wine making process to understand.
We see a correlation of 0.099 between pH and quality, which is not very strong. Many different kinds of acid contribute to pH, however, so examining each of the acidities individually should show us more about the nuances in terms of their relationships with quality.
Fixed Acidity
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.800 6.300 6.800 6.855 7.300 14.200
##
## Pearson's product-moment correlation
##
## data: wf$fixed.acidity and wf$quality
## t = -8.005, df = 4896, p-value = 1.48e-15
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.14121974 -0.08592991
## sample estimates:
## cor
## -0.1136628Fixed acidity seems to be normally distributed, centered around a mean of 6.855. There are some outliers on the higher end that are way beyond the 75th percentile, with fixed acidities of 12 or higher.
I would expect fixed acidity’s boxplot distribution to be similar to pH’s, but there is no pronounced drop in fixed acidity like I thought there would be, though it does seem like there are less wines with high fixed acidities as quality increases (the top whisker of the boxes shrinks as quality increases).
The correlation between fixed acidity and quality is -0.11, which is somewhat strong and confirms what we see in the boxplot.
Volatile Acidity
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0800 0.2100 0.2600 0.2782 0.3200 1.1000
##
## Pearson's product-moment correlation
##
## data: wf$volatile.acidity and wf$quality
## t = -13.891, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2215214 -0.1676307
## sample estimates:
## cor
## -0.194723Volatile acid’s distribution is centered on its mean of around 0.28, though it is skewed to the right. There are some wines with much higher relative volatile acidity, though they are very few in number.
In the boxplots, we see a marked drop in the distribution of volatile acidity as quality increases from low to medium, and then a sort of plateau from medium to high. The drop in volatile acidity is expected, though I am not sure why it plateaus at medium quality. Perhaps past that point, volatile acidity stops affecting the taste, but too much of it has a negative effect on taste.
The correlation between quality and volatile acidity is -0.19, which is quite strong and confirms what we see in our boxplots. Increased volatile acidity decreases wine quality, overall.
Citric Acid
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.2700 0.3200 0.3342 0.3900 1.6600
##
## Pearson's product-moment correlation
##
## data: wf$citric.acid and wf$quality
## t = -0.6444, df = 4896, p-value = 0.5193
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.03720595 0.01880221
## sample estimates:
## cor
## -0.009209091Citric acid is distributed pretty normally around its mean of 0.33, but it has some outliers on the right side, with some wines having over 1.5 g/L of citric acid.
I would expect extremes of citric aciditiy to be inversely correlated with the quality of the wines (too sour, not sour enough), but I am not a wine afficianado. The boxplot seems to confirm this - the distribution of citric acid becomes markedly more concentrated around what seems to be the overall mean (it does not shift much throughout all the boxplots). This is probably the optimal citric acid level for a wine.
The correlation between citric acid and quality is only -0.0092, though this is not a big deal. What we see is a gradual increase in the concentration of values as quality increases, rather than a change in the actual values, so the correlation test would not be expected to show this trend.
Residual Sugar
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.600 1.700 5.200 6.391 9.900 65.800
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.700 1.350 2.700 4.821 7.500 17.550## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.800 2.075 4.300 5.628 8.150 14.800##
## Pearson's product-moment correlation
##
## data: wf$residual.sugar and wf$quality
## t = -6.8603, df = 4896, p-value = 7.724e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.12524103 -0.06976101
## sample estimates:
## cor
## -0.09757683Sugar is distributed somewhat evenly, though it spikes in count towards its very lower end. Most wines have very little sugar. There are some outliers with over 20 g/L of sugar, which is why I plot another histogram that removes the most egregious outliers.
I would have expected sugar levels to have some sort of distinctive distribution based on wine quality, but the boxplot is quite strange. Both high and low quality wines tend to have very lower sugar, but medium-low shows a sudden jump in mean sugar level, which decreases as quality increases until we reach a mean of around 5.6 g/L for high quality wines. The median is 4.3 g/L, though, which suggests that some outliers heavily skew the average - this is the case for low quality wines as well, as well as for all wines, so it is probably the case that every quality has some wines that have a lot of sugar relative to other wines.
Perhaps low sugar is desirable, but a combination of other factors makes some wines with low sugar content low quality. Perhaps the wine making process naturally creates less sugar as quality increases - maybe because fermentation uses up more and more sugar. The correlation between sugar and quality is -0.097, which confirms what we see in the boxplot.
Chlorides
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00900 0.03600 0.04300 0.04577 0.05000 0.34600
##
## Pearson's product-moment correlation
##
## data: wf$chlorides and wf$quality
## t = -15.024, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2365501 -0.1830039
## sample estimates:
## cor
## -0.2099344Salt content is also distributed pretty closely around its median of 0.043. There are some outliers to the right - removing them and replotting shows us a more precise picture of the distribution. It seems that the distribution is slightly skewed to the right - there are relatively more wines with lower salt contents than there are wines with higher salt contents.
The boxplots show a marked decrease in salt content as quality increases. Clearly, having less salt is better for taste. We know from experience that small additions of salt to a dish can have very large effects on the overal taste, and wine should be no different. The correlation between salt content and quality is -0.21, which is pretty strong.
Free Sulfur Dioxide
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.00 23.00 34.00 35.31 46.00 289.00
##
## Pearson's product-moment correlation
##
## data: wf$free.sulfur.dioxide and wf$quality
## t = 0.57085, df = 4896, p-value = 0.5681
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.01985292 0.03615626
## sample estimates:
## cor
## 0.008158067Free sulfur dioxide has a mean of 35.31 and a median of 34.00. We can tell from the difference in median and mean that there will be outliers, and the histogram confirms this. Some wines have very high sulfur dioxide levels, though they are few. Removing them shows a normal distribution that is slightly skewed to the right.
The thing with sulfur dioxide is that it seems like too much of it will negatively affect the odor of the wine, and thus the quality, but too little of it means the wine has trouble keeping fresh for longer periods of time. The question is whether that actually matters in this dataset, since we have no information on when these wines were produced and thus on the freshness. However, the boxplot shows that low quality wines have very low levels of sulfur dioxide (so perhaps they do not taste as fresh), and as quality increases, the range of free sulfur dioxide levels shrinks, which lends evidence to my initial intuitions. High quality wines must have a relatively small range of possible free sulfur dioxide levels.
The correlation between free sulfur dioxide and quality is very low, however - only 0.0082. Still, the boxplot seems to show that it is related in some way to quality, so we will investigate further.
Total Sulfur Dioxide
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 9.0 108.0 134.0 138.4 167.0 440.0
##
## Pearson's product-moment correlation
##
## data: wf$total.sulfur.dioxide and wf$quality
## t = -12.418, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2017563 -0.1474524
## sample estimates:
## cor
## -0.1747372Total sulfur dioxide is very normally distributed around its mean of 138.4, with a smattering of outliers on the right. Removing them just shows us an incredibly normal distribution of values.
There does not seem to be a pattern in the boxplots. Low quality wines have similar average levels of total sulfur dioxide as high quality wines do, though there is a jump movin from low to medium-low that then steadily decreases until medium-high. Perhaps high quality wine requires low total levels of sulfur dioxide so that taste of the actual wine is not affected, but requires higher levels of gaseous sulfur dioxide for some “zest” in the aroma of the wine. We already know that low quality wines have much lower levels of free sulfur dioxide, so this is a possible explanation. Overall, though, the correlation between quality and total sulfur dioxide is -0.17.
Sulphates
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2200 0.4100 0.4700 0.4898 0.5500 1.0800
##
## Pearson's product-moment correlation
##
## data: wf$sulphates and wf$quality
## t = 3.7613, df = 4896, p-value = 0.000171
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02571007 0.08156172
## sample estimates:
## cor
## 0.05367788Sulphate level is skewed to the right, though centered around its mean of 0.4898.
The boxplot does not really tell us anything. The distribution seems to stay roughly similar throughout all quality levels. The very low correlation of 0.054 seems to confirm that we will need to investigate the relation between sulphate level and other features to glean further insights.
Density
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.9871 0.9917 0.9937 0.9940 0.9961 1.0390
##
## Pearson's product-moment correlation
##
## data: wf$density and wf$quality
## t = -22.581, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3322718 -0.2815385
## sample estimates:
## cor
## -0.3071233Density is pretty normally distributed around its mean of 0.9940, with a couple of outliers on the higher end. This is very close to 1, which is what we would expect due to wine being composed mostly of water. The mean being slightly lower than water is expected due to alcohol being less dense than water. However, there are some outliers that are actually much denser than water, which is probably due to them having very high levels of sugar and/or other solubles.
I do not think density itself is a factor in wine quality - it is probably highly correlated with other features such as salt content, alcohol content, and sugar, and thus any relation we see between density and quality is probably due to those other factors rather than density itself. Thus, the high correlation of -0.307 we see between density and quality is something we should take with a grain of salt.
The boxplot shows a general decrease in density as wine quality goes up. Perhaps higher quality wines have higher alcohol contents. This offers the perfect segue to our last feature examination, which is of alcohol.
Alcohol
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.00 9.50 10.40 10.51 11.40 14.20
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.50 11.00 12.00 11.65 12.60 14.00## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.00 9.40 10.10 10.17 10.80 13.50##
## Pearson's product-moment correlation
##
## data: wf$alcohol and wf$quality
## t = 33.858, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4126015 0.4579941
## sample estimates:
## cor
## 0.4355747Alcohol’s distribution is slightly skewed to the right - most wines have lower rather than higher alcohol contents. The overall mean is 10.51% alcohol.
The boxplots for alcohol are what is most interesting - they show, by far, the clearest trend of a feature in relation to quality. The higher than quality, the higher than alcohol content. In fact, the IQR of low and medium-low have no overlap at all with that of high quality wine. This also is a possible explanatory factor in why lower density is correlated with higher wine quality. The correlation between quality and alcohol is 0.44, the highest we have seen thus far.
Summary of initial findings
As of right now, alcohol content seems to be the most strongly correlated with wine quality. Just as a recap, here are the features with relatively strong correlations with quality: * alcohol - correlation = 0.44 * density - correlation = -0.31 * chlorides - correlation = -0.21 * volatile.acidity - correlation = -0.19 * total sulfur dioxide - correlation = -0.17 * fixed.acidity - correlation = -0.11
Citric acid seems to drill in on a certain “sweet spot” value as quality increases - the IQR of its distribution shrinks as quality increases.
Deeper Exploration - Investigating Correlations Between Features
A bit of grouping
## Source: local data frame [5 x 12]
##
## quality_level median_fixed_acidity median_volatile_acidity
## 1 low 6.9 0.32
## 2 medium-low 6.8 0.28
## 3 medium 6.8 0.25
## 4 medium-high 6.7 0.25
## 5 high 6.8 0.26
## Variables not shown: median_citric_acid (dbl), median_total_acidity (dbl),
## median_alcohol (dbl), median_sugar (dbl), median_ph (dbl),
## median_chlorides (dbl), median_total_so2 (dbl), median_free_so2 (dbl),
## median_sulphates (dbl)Here, I have done some aggregations on the various features. I have also created a new variable called total acidity, which is the sum of citric, fixed, and volatile acidity.
Investigating Acidity
##
## Pearson's product-moment correlation
##
## data: wf$fixed.acidity and wf$volatile.acidity
## t = -1.5886, df = 4896, p-value = 0.1122
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.050671536 0.005312543
## sample estimates:
## cor
## -0.02269729
##
## Pearson's product-moment correlation
##
## data: wf$citric.acid and wf$fixed.acidity
## t = 21.137, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2633067 0.3146389
## sample estimates:
## cor
## 0.2891807##
## Pearson's product-moment correlation
##
## data: wf$citric.acid and wf$volatile.acidity
## t = -10.578, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1767384 -0.1219760
## sample estimates:
## cor
## -0.1494718
##
## Pearson's product-moment correlation
##
## data: wf$total.acidity and wf$pH
## t = -33.388, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4531918 -0.4075605
## sample estimates:
## cor
## -0.4306513The correlation between fixed and volatile acidity is pretty small, but there is a correlation between citric acid and fixed acidity of 0.29. This is positive, unlike the correlation between citric acid and volatile acidity of -0.15. I am not sure why that is, but it seems interesting that more citric acid increases fixed acidity but decreases volatile acidity.
As expected, total acidity is negatively correlated with pH - more acids (obviously) mean lower pH.
Sugar, Alcohol, and Quality
##
## Pearson's product-moment correlation
##
## data: wf$alcohol and wf$residual.sugar
## t = -35.321, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4726723 -0.4280267
## sample estimates:
## cor
## -0.4506312What seems interesting here is that while plotting sugar on its own against quality does not show much of a correlation, plotting residual sugar against alcohol and then coloring by quality seems to show that higher quality wines, which tend to have higher alcohol contents, also tend to have lower sugar levels than wines with lower alcohol contents. It is clear that plotting sugar with alcohol content strengthened both features.
The correlation between alcohol and sugar is -0.45, which is very strong. As alcohol increases, sugar levels tend to decrease, which confirms what we see in our plot. Perhaps this is a result of wine-creating bacteria consuming more sugar to produce more ethanol.
Sugar, Alcohol, Chlorides, and Density
##
## Pearson's product-moment correlation
##
## data: wf$residual.sugar and wf$density
## t = 107.87, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8304732 0.8470698
## sample estimates:
## cor
## 0.8389665
##
## Pearson's product-moment correlation
##
## data: wf$alcohol and wf$density
## t = -87.255, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.7908646 -0.7689315
## sample estimates:
## cor
## -0.7801376
##
## Pearson's product-moment correlation
##
## data: wf$chlorides and wf$density
## t = 18.624, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2308679 0.2831779
## sample estimates:
## cor
## 0.2572113As expected, both alcohol content and residual sugar are highly correlated with density. If we were to create a linear regression model for quality, we should avoid having all three of these variables in the model, as multicollinearity would become a significant problem. Salt content is also correlated with density, though to a lesser extent than the other two features.
Investigating salt content
##
## Pearson's product-moment correlation
##
## data: wf$chlorides and wf$residual.sugar
## t = 6.2299, df = 4896, p-value = 5.057e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.06082916 0.11640188
## sample estimates:
## cor
## 0.08868454
##
## Pearson's product-moment correlation
##
## data: wf$chlorides and wf$alcohol
## t = -27.016, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3843183 -0.3355673
## sample estimates:
## cor
## -0.3601887What is interesting is the inverse correlation between alcohol and chlorides, which I would not have expected. It seems that there are no wines with low alcohol content and low chloride levels and no wines with high alcohol content and high chloride levels. I am not sure why that is - perhaps it is a side effect of making wine with high alcohol content, or that high quality wines are produced with the goal of high alcohol content and low salt content in mind. Regardless, they are correlated, so we should bear that in mind while constructing a model so as to keep multicollinearity at a minimum.
Investigating sulfate levels
##
## Pearson's product-moment correlation
##
## data: wf$sulphates and wf$total.sulfur.dioxide
## t = 9.5019, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1069590 0.1619585
## sample estimates:
## cor
## 0.1345624##
## Pearson's product-moment correlation
##
## data: wf$sulphates and wf$free.sulfur.dioxide
## t = 4.1508, df = 4896, p-value = 3.369e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.03126264 0.08707928
## sample estimates:
## cor
## 0.05921725
##
## Pearson's product-moment correlation
##
## data: wf$free.sulfur.dioxide and wf$total.sulfur.dioxide
## t = 54.645, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.5977994 0.6326026
## sample estimates:
## cor
## 0.615501The level of sulphates in a wine does not seem to be very closely related to the amount of sulfur dioxide both in gaseous and dissolved form, though this is expected because the readme for the dataset says that sulphate level contributes only a small amount to sulfur dioxide.
As expected, total sulfur dioxide and free sulfur dioxide are pretty strongly correlated.
Summary of findings so far
First, let us talk about the features other than the feature of interest that are correlated with each other. Some were obvious and expected, others are not: - alcohol and density - sugar and density - chlorides and alcohol - total sulfur dioxide and free sulfur dioxide - all the various acidities with pH
Now, let us list how these features relate to quality: - higher alcohol and higher quality - lower sugar and higher quality - lower total sulfur dioxide and higher quality - lower acidity and higher quality - lower salt content and higher quality
With this information, we can improve on our expectations of what makes for a high quality wine. Good wines tend to have higher alcohol contents, fruitier flavor (due to higher citric acid content), lower sugar levels, lower salt levels, lower sulfur dioxide levels, and lower overall acidity. I have left out features such as density, which is too strongly correlated with more important features such as alcohol content and chloride levels, and sulphates, which does not seem to be correlated with quality and is only very slighty correlated with total sulfur dioxide.
Quick Model
##
## Calls:
## m1: lm(formula = alcohol ~ quality, data = wf)
## m2: lm(formula = alcohol ~ quality + volatile.acidity, data = wf)
## m3: lm(formula = alcohol ~ quality + volatile.acidity + chlorides,
## data = wf)
## m4: lm(formula = alcohol ~ quality + volatile.acidity + chlorides +
## residual.sugar, data = wf)
## m5: lm(formula = alcohol ~ quality + volatile.acidity + chlorides +
## residual.sugar + total.sulfur.dioxide, data = wf)
##
## ============================================================================
## m1 m2 m3 m4 m5
## ----------------------------------------------------------------------------
## (Intercept) 6.957*** 6.166*** 7.351*** 8.085*** 8.963***
## (0.106) (0.123) (0.127) (0.114) (0.117)
## quality 0.605*** 0.648*** 0.567*** 0.526*** 0.493***
## (0.018) (0.018) (0.017) (0.015) (0.015)
## volatile.acidity 1.936*** 2.043*** 2.264*** 2.365***
## (0.158) (0.150) (0.132) (0.127)
## chlorides -16.128*** -14.541*** -12.681***
## (0.693) (0.612) (0.594)
## residual.sugar -0.098*** -0.076***
## (0.003) (0.003)
## total.sulfur.dioxide -0.007***
## (0.000)
## ----------------------------------------------------------------------------
## R-squared 0.190 0.214 0.292 0.452 0.495
## adj. R-squared 0.190 0.214 0.292 0.451 0.495
## sigma 1.108 1.091 1.036 0.912 0.875
## F 1146.395 666.007 673.471 1008.012 959.723
## p 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -7450.661 -7376.455 -7119.517 -6493.901 -6291.857
## Deviance 6009.118 5829.768 5249.127 4065.773 3743.809
## AIC 14907.323 14760.910 14249.034 12999.801 12597.714
## BIC 14926.812 14786.896 14281.517 13038.781 12643.190
## N 4898 4898 4898 4898 4898
## ============================================================================Modeling
In the end, using just a pretty basic linear model, we get an R-squared of 0.496, which is not too shabby. Of course, this is far from a perfect model - a linear regression simply cannot capture all the subtleties of the data. I also included both chlorides and alcohol in the model, even though I already know that they are correlated with each other. Thus, there is some degree of multicollinearity that is negatively affecting the truth of the model.
Final Plots and Summary
Plot One
Description One
This plot shows very obviously that there is definitely a trend towards higher alcohol content as wine quality increases. Just having a higher alcohol content seems to be a huge factor in determining wine quality - the entire boxplot moves up for each increase in quality level, which is not something I would have expected. It really makes me wonder why exactly alcohol is so strongly correlated with wine quality, and whether that bears out in real life. This plot sparked much of the exploration in regard to whether other features were strongly correlated with alcohol - is higher alcohol content a result of a general higher-quality wine making process, or is it purposefully sought after in the wine making process? I spent much of my time trying to explore this angle in this report.
Plot Two
Description Two
I selected these first two plots because they reveal quirks of the data that you wouldn’t have been able to see otherwise. During my EDA, it was hard to see whether sugar content related at all to wine quality - different levels of sugar content seemed to be distributed quite evenly across all wine qualities. However, this plot immediately reveals two things: (1) higher quality alcohol does, in fact, have lower sugar levels, and (2) there are no high alcohol and high sugar content wines. The insights this plot offered me meant I now was willing to use residual sugar as a feature in the linear regression model I hoped to build, since it was clearly correlated with wine quality. And this paid off - adding residual.sugar to my linear model raised the R-squared value (unadjusted) from 0.292 to 0.453.
Plot Three
Description Three
This reveals a relationship between features that I had not expected at all. For some reason, alochol content seems to be inversely correlated with salt content - and high quality wines are overwhelmingly concentrated in the area of the plot where salt content is low and alcohol percentage is high.
Reflection
This project was intimidating at first because there were so many features. Which ones should I concentrate on? Which ones would actually have any effect? And once I plotted the distributions of each with regard to quality, I did not come out as elucidated as I had thought I would be - only alcohol and perhaps salt seemed to contribute in any way to wine quality. This was unlike the diamond data set, in which features were fewer and there were universally defined metrics for what made a better diamond.
Still, there were a few common sense hunches that I had regarding what would affect wine quality - I feel that oftentimes, our own intuition is where we begin in such investigations, and in the process of confirming or invalidating those intuitions, we discover new quirks and trends that would not have occurred to us without such exploration. That is what happened with me - I felt that sugar levels and acidity ought to have some significant effect on wine quality.
After trying various plots with sugar levels, I was about ready to give up. There seemed to be no rhyme nor reason with sugar content across different quality wines. However, when I finally plotted sugar vs. alcohol content and colored the points by quality, sugar’s inverse relationship with wine quality finally revealed itself. Needless to say, I was pleased. However, this plot also revealed sugar’s inverse correlation with alcohol, which made me wonder why exactly would there be a relationship between alcohol and sugar? Is it because of the fermentation process that converts sugar into ethanol, and therefore the higher the alcohol content, the lower the sugar level?
This induced me to investigate further the relationship between alcohol and other features, and I found, to my surprise, that chlorides and alcohol were also inversely correlated. Wines with high alcohol contents also had low salt contents, and were generally rated higher, than wines with low alcohol contents with high salt contenst, which were generally rated lower. In fact, there seemed to be a relative dearth of wines that had both high alcohol and high salt contents as well as both low alcohol and low salt contents. This begs the same question that the discovery of sugar’s relationship with alcohol evoked: was this a result of the wine making process that naturally meant high quality wines had high alcohol contents and low salt contents, or was this due to wine makers purposely choosing to make wines with these characteristics? I do not think this is a question that can be answered with EDA alone - it would require an understanding of the wine making process as well.
Once I got the ball rolling in mixing and matching features to see if anything strange and interesting popped out, it was a relatively straightforward process to see how acidity related to wine quality. Strangely enough, it turned out that higher citric acid was correlated with higher wine quality even though overall acidity (as measured by pH and my total acidity variable) was correlated with lower wine quality. I attributed this to higher citric acid levels making wines taste fruitier. Also, total acidity was dominated by fixed acidity - citric acid was a small enough component of total acidity that its level was nearly neglible in determining pH, so this was actually a finding that made sense. Too acidic of a wine probably tastes bad, but fruitier wine tastes better.
Looking forward
There are still many things that could be done. There are some combinations of features that I have not plotted - namely, that between sulphates and sulfur dioxide levels with density, and whether that could change anything in my analysis. Perhaps using more boxplots would also reveal some interesting things.
Also, if I were to spend more time on this, I would likely create more robust models for predicting wine quality - using naive Bayes, or vector models, or a logistic regression. My linear model had decent results, but is not as good of a model as a model could be.
I would like to actually compare white wines with red wines - there would probably be a lot of interesting insights into the character of these two wines, in terms of their various acidities, alcohol contents, sugar levels, etc., and what makes for a high quality red or white wine.